Moving over land -- from the United States to Mexico, for example -- is fairly straighforward. When your move requires ocean passage, however, you have four shipping options (excluding air freight).
Door to Door is an end-to-end service: the movers will pick up your stuff at your home and deliver it to your destination home. The mover will also take care of customs clearance. Unless you are very confident in your ability to manage getting your stuff to the departure port, or getting your stuff from the destination port, this is the way to go.
Port to Port will save you money but involves the most work: you are responsible for getting your household goods to the departure port and picking them up again at the destination port. You'll be responsible for dealing with customs, inspections, and port fees. This option only makes sense if you live relatively near a port in both locations.
If getting your stuff to a local port is an issue but you are able to retrieve it from the destination port, then Door to Port may be a good option. The moving company will come to your home to pick up your goods and deliver them to the port nearest your destination. If you don't have the means to pick up the stuff yourself you'll have to find a moving company in your destination country to do it for you. As one mover cautioned about both Port to Port and Door to Port, you'll have to find a moving company in a foreign country to get your stuff and bring it to you; they can charge you an arm and a leg because they realize you have no other options.
Note that Port to Port and Door to Port quotes do not include Terminal Handling Charges and other port fees, which can be significant.
Port to Door is the opposite of Door to Port -- you're responsible for getting your stuff to the departure port but the moving company will deliver it to your home at your final destination. In this scenario, the moving company will handle customs clearance.
This decision really comes down to one of ability. If you speak the language in your destination and don't mind the hassle of dealing with customs and fees yourself and, importantly, have a means to deliver and pick up your stuff from the port(s), these options may make sense.